Question

phân tích

\((a-b)(b-c)(a-c)+(a+b)(c+a)(c-b)+(b+c)(c+a)(b-a)\)

Answer 1

= (a-b)(b-c)(a-c) + (c+a)[(a+b)(c-b)+(b+c)(b-a)]

= (a-b)(b-c)(a-c) + (c+a)(ac-ab+bc-b²+b²-ab+bc-ac)

= (a-b)(b-c)(a-c) + (c+a)(-ab+bc-ab+bc)

= (a-b)(b-c)(a-c) +2 (c+a)(bc-ab)

=(a-b)(b-c)(a-c) + 2b(c+a)(c-a)

= (a-b)(b-c)(a-c) - 2b(c+a)(a-c)

= (a-c)[(a-b)(b-c) -2b(c+a)]

= (a-c)(ab-ac-b²+bc-2bc-2ab)

= (a-c)(-ab-ac-b²-bc)

= -(a-c)(ab+ac+b²+bc)

= -(a-c)(b+c)(a+b)